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272 DS perspective on statistical inferenceThe mindset of the user of DS methods is that each assignment of a (p, q, r)judgment is based on evidence. Evidence is a term of art, not a formal concept.Statistical data is one source of evidence. If the outcome of a sequence of n =10 tosses of a certain bent coin is observed to result in data HTTHHHTHTT,then each data point provides evidence about a particular toss, and querieswith (1, 0, 0) responses can be given with confidence concerning individualmargins of the 10-dimensional SSS. The user can “combine” these marginalinferences so as to respond to queries depending on subsets of the sequence,or about any interesting properties of the entire sequence.The DS notion of “combining” sources of evidence extends to cover probabilisticallyrepresented sources of evidence that combine with each other andwith data to produce fused posterior statistical inferences. This inference processcan be illustrated by revising the simple SSS of 10 binary variables toinclude a long sequence of perhaps N =10,000cointosses,ofwhichtheobservedn = 10 tosses are only the beginning. Queries may now be directed atthe much larger set of possible outcomes concerning properties of subsets, orabout any or all of the tosses, whether observed or not. We may be interestedprimarily in the long run fraction P of heads in the full sequence, then shrinkback the revised SSS to the sequence of variables X 1 ,...,X 10 , P ,whencetowork with approximate mathematics that treats N as infinite so that P maytake any real value on the closed interval [0, 1]. The resulting inference situationwas called “the fundamental problem of practical statistics” by KarlPearson in 1920 giving a Bayesian solution. It was the implicit motivation forJakob Bernoulli writing circa 1700 leading him to introduce binomial samplingdistributions. It was again the subject of Thomas Bayes’s seminal posthumous1763 note introducing what are now known as uniform Bayesian priors andassociated posterior distributions for an unknown P .My 1966 DS model and analysis for this most basic inference situation,when recast in 2013 terminology, is best explained by introducing a set of“auxiliary” variables U 1 ,...,U 10 that are assigned a uniform personal probabilitydistribution over the 10-dimensional unit cube. The U i do not representany real world quantities, but are simply technical crutches created for mathematicalconvenience that can be appropriately marginalized away in the endbecause inferences concerning the values of the U i have no direct real worldinterpretation.Each of the independent and identically distributed U i provides the connectionbetween a known X i and the target unknown P .Therelationshipsamong X i , P , and U i are already familiar to statisticians because they arewidely used to “computer-generate” a value of X i for given P .Specifically,my suggested relations areX i =1if0≤ U i ≤ P and X i =0ifP